• Rigid-body registration (linear) - 6 degrees of freedom (dof)
  • Co-registration (within the same person)
    • Cross-sectional between-sequences
    • Longitudinal within-sequence
    • Longitudinal between-sequences
• Affine registration – 12 dof
• Non-linear (> 12 dof)
  • Usually require a prior affine registration
  • Across-subject registration
  • Registration to a template
    • There are many different templates

• Rigid-body registration (linear) - 6 degrees of freedom (dof)
  • Co-registration (within the same person)
    • Cross-sectional between-sequences
    • Longitudinal within-sequence
    • Longitudinal between-sequences
• Affine registration – 12 dof
• Non-linear (> 12 dof)
  • Usually require a prior affine registration
  • Across-subject registration
  • Registration to a template
    • There are many different templates

For a voxel \(v\), the rigid transformation can be written as:

\[T_{\rm rigid}(v) = Rv + t\] where \(R =\) \[\left[\begin{array}{ccc} \cos\beta\cos\gamma& \cos\alpha\sin\gamma + \sin\alpha\sin\beta\cos\gamma & \sin\alpha\sin\gamma - \cos\alpha\sin\beta\cos\gamma \\ -\cos\beta\sin\gamma & \cos\alpha\cos\gamma - \sin\alpha\sin\beta\sin\gamma & \sin\alpha\cos\gamma + \cos\alpha\sin\beta\sin\gamma \\ \sin\beta & -\sin\alpha\cos\beta & \cos\alpha\cos\beta \end{array}\right]\]

• 6 degrees of freedom
• \(3\) associated with the translation vector: \(t=(t_x, t_y, t_z)\)
• \(3\) associated with the rotation parameters: \(\theta=(\alpha, \beta,\gamma)\).

• Pitch - Think of nodding ("yes")
• Yaw - Think of shaking head ("no")
• Roll - Think of shoulder shrugging ("I don't know")
• x – left/right
• y – forward/backward
• z – jump up/down

• Initialize an empty list and add two elements to it

l = list()
l[[1]] = c(1, 2, 4, 5)
l[[2]] = matrix(1:10, nrow = 2)
print(l)

[[1]]
[1] 1 2 4 5

[[2]]
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

• Subsetting uses double brackets:

print(l[[1]])

[1] 1 2 4 5

If a vector has names, you can also put the - Initialize an empty list and add two elements to it

x = c(first = 1, third = 14, second = 5)
print(x)

 first  third second 
     1     14      5 

x[c("third")]

third 
   14 

If a list has names, you can subset with the $

• Subsetting uses double brackets:

names(l) = c("V", "m")
l$V

[1] 1 2 4 5

With lists and vectors, there are apply functions. These apply a function to every element of the list. In this course, we will use:

• lapply - apply function and return the elements as a list
• sapply - apply function and return a "simplified" version
  • if all elements returned are a one-element vector, return a vector
  • if element 5 has 3 elements and element 4 has 4 elements, return a list

Here we will use the ms.lesion package, with the additional imaging data.

• get_image_filenames_list_by_subject - returns a list, each element is a subject, and each subject has a vector of filenames, named for each modality

library(ms.lesion)
library(neurobase)
library(extrantsr)
all_files = get_image_filenames_list_by_subject()
names(all_files)

[1] "test01"     "test02"     "test03"     "training01" "training02"
[6] "training03" "training04" "training05"

files = all_files$training01
names(files)

[1] "MPRAGE" "T2"     "FLAIR"  "PD"    

t1_fname = files["MPRAGE"]
t1 = readnii(t1_fname)

The registration function from extrantsr can register 2 images. The main arguments are:

• filename - either nifti object or filename of image to be registered (moving)
• template.file - either nifti object or filename of target image (fixed)
• typeofTransform - transformation of moving to fixed image (Rigid/Affine/SyN)
• interpolator - how are voxels averaged in fixed space

It can also perform bias correction if correct = TRUE.

For example, if we wanted to register the FLAIR to the T1 image, we would run:

library(extrantsr)
reg = registration(filename = files["FLAIR"], 
                   template.file = files["MPRAGE"],
                   typeofTransform = "Rigid", 
                   interpolator = "linear")

The output in reg would contain the transformed image and paths to the estimated transformations.

We will register scans within a visit to the T1 of that visit.

We would like to perform registration within a visit for all modalities. The extrantsr function preprocess_mri_within will do the following steps:

1. Inhomogeneity correction (N3 or N4)
   • Could also use images from previous lecture
2. Registration of the files to the first filename (T1) for all images
3. Skull_stripping using BET if desired
   • We will set this to FALSE
   • We will apply our MALF masks later

The function within_visit_registration arguments take in:

• fixed image - the image to be registered to
• moving images - images to register to the fixed
• typeofTransform - transformation of moving to fixed image (Rigid/Affine)
• interpolator - how are voxels averaged in fixed space

and outputs a list of transformations (fwdtransforms) and output filenames (outfile)

res = within_visit_registration(
  fixed = files["MPRAGE"],
  moving = files[c("T2", "FLAIR", "PD")],
  correct = TRUE, correction = "N4",
  typeofTransform = "Rigid", 
  interpolator = "Linear"
)
output_imgs = lapply(res, function(x) x$outfile)
names(output_imgs) = c("T2", "FLAIR", "PD")
out = c(MPRAGE = list(t1), output_imgs)

double_ortho(out$MPRAGE, out$T2 )

The multi_overlay function takes in a list of images and then plots one slice across modalities:

multi_overlay(out)

• Overall, there seems to be good overlap after registration
• It is usually beneficial to do inhomogeneity correction before registration.
  • just set correct = TRUE or pass in the bias-corrected images

Applying a Brain mask to all registered images

Now that the images are in the same space as the T1, if we skull-strip the T1 image (we did with MALF), we can apply this mask to those images to extract brain tissues using the neurobase::mask_img command:

mask = readnii("../output/training01_01_mprage_mask.nii.gz") # MALF mask 
masked_imgs = lapply(out, mask_img, mask)

orthographic(masked_imgs$FLAIR)

orthographic(masked_imgs$T2)

• Registration within a subject can be done in R
  • registration wraps around the reading/writing of images and applying transformations (uses ANTsR functions)
  • double_ortho, ortho2, and multi_overlay can provide some basic visual checks to assess registration quality
  • preprocess_mri_within and preprocess_mri_across are general wrapper functions to process MRI data
• Once images are registered in the same space, operations can be applied to all the images, such as:
  • Masking with a brain mask
  • Transforming images to new spaces with one modality

• Co-registration requires a few degrees of freedom (usually 6)
  • sequences from the same individual/brain are more alike than images from different subjects
• Example analyses that do not require a reference template
  • Identify location-specific longitudinal changes within an individual
  • Tissue class or structural segmentation
  • Analysis of indvidual-subject change in intensities

We have only done registration within a subject, but many times you want to perform a population-level analysis. This requries registration to a template:

• The registration can be done for this as well, just the template.file is now the template image and filename is the subject image.
  • other files (in the same space) can be transformed using the other.files and other.outfiles arguments. Or:
  • ants_apply_transforms can be used to apply this transformations to the other files

http://johnmuschelli.com/imaging_in_r